Elliptic curve isogeny class with LMFDB label 31200.ba (Cremona label 31200c)

• Label: 31200.ba
• Number of curves: $4$
• Conductor: $31200$
• CM: no
• Rank: $1$

Elliptic curves in class 31200.ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
31200.ba1	31200c4	\([0, -1, 0, -5688008, 5221701012]\)	\(2543984126301795848/909361981125\)	\(7274895849000000000\)	\([2]\)	\(1179648\)	\(2.5885\)
31200.ba2	31200c3	\([0, -1, 0, -2938008, -1897486488]\)	\(350584567631475848/8259273550125\)	\(66074188401000000000\)	\([2]\)	\(1179648\)	\(2.5885\)
31200.ba3	31200c1	\([0, -1, 0, -406758, 56638512]\)	\(7442744143086784/2927948765625\)	\(2927948765625000000\)	\([2, 2]\)	\(589824\)	\(2.2419\)	\(\Gamma_0(N)\)-optimal
31200.ba4	31200c2	\([0, -1, 0, 1304367, 407419137]\)	\(3834800837445824/3342041015625\)	\(-213890625000000000000\)	\([2]\)	\(1179648\)	\(2.5885\)

Rank

The elliptic curves in class 31200.ba have rank \(1\).

Complex multiplication

The elliptic curves in class 31200.ba do not have complex multiplication.

Modular form 31200.2.a.ba

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.